A0623
Title: Model selection confidence sets for variable selection in regression via Vuong-type tests
Authors: Davide Ferrari - Free University of Bozen/Bolzano (Italy) [presenting]
Abstract: A fundamental challenge in regression modeling is selecting the set of relevant predictors from a potentially large collection of candidate variables. Traditional approaches choose a single best model using information criteria or penalized likelihood methods. However, models with different variable subsets often yield similar fits, leading to substantial model selection uncertainty and making it difficult to identify the optimal set of predictors. The model selection confidence set (MSCS) is introduced for variable selection in regression, a set-valued estimator that, with a predefined confidence level, includes the true model across repeated samples. Unlike previous approaches, the method builds these sets using a sequence of Vuong's type tests that accommodate comparisons among both nested and non-nested models. To screen models, each candidate is compared through these tests to a reference model selected by an arbitrary model selection method. Rather than selecting a single model, the MSCS identifies all plausible models that are at least as plausible as this selected reference. Theoretical guarantees are provided for asymptotic coverage, and its practical advantages are demonstrated through simulations and real data analysis.
